Washington
— The list of troubles between China and the United States seems to grow ever longer. The latest potential flap involves a Pan American World Airways plan next month to reopen its flights to Taiwan, service that the airline dropped five years ago in the hope of doing better business in China.

The recent highly publicized troubles have tended to obscure the larger strategic and economic relationship between the world's most populous nation and its most technologically advanced. The real news in US-China relations may not be the strains that have tested them so frequently over the past few years, but the aspects of the relationship that are thriving.

Almost imperceptibly, through developments that don't make front-page headlines, the two nations are demonstrating that there is a shock-absorbing depth to the relationship.

This has been a year for the exchange of high-level trade and scientific missions that seem to be strengthenil11l,0,13l,5ping the US-China connection. And throughout the conflict over Chinese tennis star Hu Na's request for asylum in the US, the Chinese have demonstrated that they don't want political shocks to damage trade relations, educational programs, and scientific and technological exchanges.

Most important, the Chinese have consistently indicated that they share with the US a certain strategic outlook, including a conviction that the Soviet Union constitutes the greatest danger to the two nations and to stability in the world.

To be sure, irritants in the US-China relationship remain. Aside from the US decision last month to grant political asylum to Hu Na, the list includes a continuing disagreement over China's textile exports to the US, American restrictions on high technology transfers, a US federal court decision against China on a railway bonds claim, and China's request to enter the Asian Development Bank and thus oust Taiwan.

The biggest conflict of all is over continuing American arms sales to Taiwan.

Underlying all the problems and frustrations is a mistrust of President Reagan on the part of a number of Chinese officials. The feelings stem from Mr. Reagan's days as a presidential candidate. He has never hidden his affection for Taiwan. But in the end, President Reagan has acted quite differently from candidate Reagan. According to a number of China watchers, he has gone about as far to accommodate Peking as a second-term President Carter would have done.

But Reagan has given the impression that his foreign-policy advisers had to drag him kicking and screaming into an appreciation of the importance of US-China relations.

At the same time, say US analysts, the Chinese and Americans have come to recognize that there are limits to the relationship.

The latest manifestation of the beneficial side of the relationship came May 11, when presidential science adviser George A. Keyworth signed four new agreements with the Chinese at the Great Hall of the People in Peking. The new accords point to US-China cooperation in aeronautics, transportation, biomedical sciences, and nuclear physics. These brings to 21 the total of such accords signed over the past four.

In the fields of culture and sports, the Chinese canceled ''official'' exchanges for the rest of the year in reaction to the American decision on Hu Na. But so many ''unofficial'' arrangements have been made in recent years that one still finds any number of exchanges taking place. One example: US playwright Arthur Miller's coaching of Chinese actors and actresses in a Chinese production of ''Death of a Salesman.''

China's recent unprecedented negotiations with US ally South Korea over a hijacked Chinese airliner are seen here as yet another sign of Peking's reasonableness.

Three tests of the US-China relationship are now in the making:

* After a visit to Japan, Commerce Secretary Malcolm Baldrige leaves for Peking May 21 to serve as cochairman of the first session of the US-China Joint Commission on Commerce and Trade. Mr. Baldrige has indicated that he is thinking big. He would like to increase the US role in the development of China's offshore oil reserves, huge coal deposits, and what he describes as the largest reserve of hydroelectric power in the world. The Commerce secretary also has his eye on cooperation in the development of China's telecommunications.

* Another round of textile negotiations between the two nations is expected to take place before long. Senior US officials say the two sides are now close to an agreement.

* American restrictions on the transfer of technology to China have been one of the great irritants in the relationship. US bureaucrats in all of the agencies involved are now intensively reviewing the procedures and paperwork. The aim is to streamline the process. Given the ways of bureaucracies, that is easier said than done. But as one of the officials concerned put it, ''We should not be sitting on applications for two or three years.''